The Rangers' thinking would be to deal from a position of strength and turn the closer's role over to Joakim Soria, according to Rosenthal. Texas could also shift Alexi Ogando back into a setup role if Nathan was dealt. The team also expects to have Neftali Feliz, who is recovering from Tommy John surgery, back in close to a month.

Texas has reportedly been looking to add some offensive help, and the team could expand their trade possibilities if Nathan was made available, according to Rosenthal.

Nathan, 38, is 32-for-34 in save opportunities this season and has a 1.73 ERA for the Rangers. Nathan is owed about $2.5 million for the rest of the season, Rosenthal notes. Nathan also has a $9 million club option for 2014, but he can void it to become a free agent if he finished at least 55 games this season. So far, Nathan has finished 39 games.